Tri-bimaximal mixing from twisted Friedberg–Lee symmetry

We investigate the Friedberg–Lee (FL) symmetry and its promotion to include the μ–τ symmetry, and call this the twisted FL symmetry. Based on the twisted FL symmetry, two possible schemes are presented toward the realistic neutrino mass spectrum and the tri-bimaximal mixing. In the first scheme, we suggest the semi-uniform translation of the FL symmetry. The second one is based on the S ₃ permutation family symmetry. The breaking terms, which are twisted FL symmetric, are introduced. Some viable models in each scheme are also presented.     

On long-range curve crossings

The V symmetry coupling coefficients for the icosahedral double group are generated from the behaviour of a minimum number of |JM> ket vectors where the symmetry coupling coefficients are defined as analogues of the Racah V coefficients. The phases are determined from the way the irreducible representations for the specific J values are defined. An investigation of the symmetry properties of the system by a translation of the |JM> ket vectors for integral J values is examined. The handling of the irreducible-tensor method in group notation is discussed briefly.     

Ground states of two-dimensional quasicrystals

Hamiltonians for nonperiodic tilings are considered. It is shown that the quasicrystalline tiling obtained by the cut-and-strip method from aD-dimensional cubic lattice may bs a ground state only if the tiling possesses a high orientational symmetry: the (2,D)-quasicrystal should haveD-fold symmetry ifD is even and 2D-fold symmetry ifD is odd. For interactions of a finite range the restrictions are stronger: only a (2, 5)-quasicrystal (Penrose tiling) may be a stable ground state.     

On the Non-Lorentz-Invariance of <Emphasis Type="SmallCaps">M.W. Evans’</Emphasis><Emphasis Type="Italic">O</Emphasis>(3)-Symmetry Law

In 1992 M.W. Evans proposed the O(3) symmetry of electromagnetic fields by adding a constant longitudinal magnetic field to the well-known transverse electric and magnetic fields of circularly polarized plane waves, such that certain cyclic relations of a so-called O(3) symmetry are fulfilled. Since then M.W. Evans has elevated this O(3) symmetry to the status of a new law of electromagnetics. As a law of physics must be invariant under admissible coordinate transforms, namely Lorentz transforms, in 2000 he published a proof of the Lorentz invariance of O(3) symmetry of electromagnetic fields. As will be shown below this proof is incorrect; more, after simple correction it will turn out here that the O(3) symmetry cannot be Lorentz invariant.     

Partial Wave Crossing Relations for Meson-Baryon Scattering

Three different types of relations for meson-baryon partial wave amplitudes following from the s ↔ u crossing symmetry of the invariant amplitudes are investigated: i) the partial wave crossing relations directly derived from the s ↔ u crossing symmetry and the partial wave projection, ii) the partial wave crossing relations following from a combined use of s ↔ u crossing symmetry and analyticity, and iii) the crossing sum rules, which are a direct consequence of the s ↔ u crossing symmetry. The kernels entering the crossing relations i) and ii) are given in an analytic form, valid for arbitrary angular momentum. Their properties are studied in detail. By means of the partial wave crossing relations ii) it is demonstrated that u-channel exchange of a resonance leads to a resonance-like behaviour of the partial wave amplitudes on the crossed physical cut. This phenomenon is described in terms of “pseudoresonances”. Finally the crossing sum rules iii) and their practical use are thoroughly discussed, and they are compared with the partial wave crossing relations i) and ii). Special attention is paid to the crossing symmetry constraints on the S-wave amplitudes. As a result of these investigations we present a crossing symmetric ansatz for these amplitudes which gives a more reliable parametrization than the usual effective range approximation.     

The symmetry properties and collinearity of the magnetogyric,hyperfine splitting and magnetic susceptibility tensors

The symmetry properties of g and A cannot be elicited using invariance properties, due to their special nature, and are found using the properties of a Kramers doublet. It is shown that the collinearity of g and A depends on the molecule having at least C ₂ with σ _v or C ₂′ symmetry elements. The symmetry properties of x are found from those of g. The conditions for collinearity of the tensors and the consequences of non-collinearity are discussed, with examples.     

On symmetries and averaging of the G-equation for premixed combustion

It is demonstrated that the G-equation for premixed combustion admits a diversity of symmetries properties, i.e. invariance characteristics under certain transformations. Included are those of classical mechanics such as Galilean invariance, rotation invariance and others. Also a new generalized scaling symmetry has been established. It is shown that the generalized scaling symmetry defines the physical property of the G-equation precisely. That is to say the value of G at a given flame front is arbitrary. It is proven that beside the symmetries of classical mechanics, particularly the generalized scaling symmetry uniquely defines the basic structure of the G-equation. It is also proven that the generalized scaling symmetry precludes the application of classical Reynolds ensemble averaging usually employed in statistical turbulence theory in order to avoid non-unique statistical quantities such as for the mean flame position. Finally, a new averaging scheme of the G-field is presented which is fully consistent with all symmetries of the G-equation. Equations for the mean G-field and flame brush thickness are derived and a route to consistent invariant modelling of other quantities derived from the G-field is illustrated. Examples of statistical quantities derived from the G-field both in the context of Reynolds-averaged models as well as subgrid-scale models for large-eddy simulations taken from the literature are investigated as to whether they are compatible with the important generalized scaling symmetry.     

Specific propagation directions of acoustic waves for piezoelectric and nonpiezoelectric media

I reanalyze the problem of the existence of longitudinal normals inside the symmetry planes of piezoelectric crystals belonging to the symmetry class mm2. The equations determining components of longitudinal normals situated outside the symmetry planes for media of this symmetry are discussed. It is proven that nonpiezoelectric media of rhombic symmetry could have 4 or 8 distinct acoustic axes. Examples of nonpiezoelectric elastic media of monoclinic symmetry without acoustic axes are given. The method of determination of the components of acoustic axes for piezoelectric media of arbitrary symmetry is presented. With the help of this method, I discuss the problem of acoustic axes for piezoelectric media of the symmetry class mm2. The text was submitted by the author in English.     

Gauge Formulation for Two Potential Theory of Dyons

Dual electrodynamics and corresponding Maxwell’s equations (in the presence of monopole only) are revisited from the symmetry of duality and gauge invariance. Accordingly, the manifestly covariant, dual symmetric and gauge invariant two potential theory of generalized electromagnetic fields of dyons has been developed consistently from U(1)×U(1) gauge symmetry. Corresponding field equations and equation of motion are derived from Lagrangian formulation adopted for U(1)×U(1) gauge symmetry for the justification of two four potentials of dyons.     

$\mathcal{PT}$ Symmetry in Statistical Mechanics and the Sign Problem

Generalized PT\mathcal{PT} symmetry provides crucial insight into the sign problem for two classes of models. In the case of quantum statistical models at non-zero chemical potential, the free energy density is directly related to the ground state energy of a non-Hermitian, but generalized PT\mathcal{PT}-symmetric Hamiltonian. There is a corresponding class of PT\mathcal{PT}-symmetric classical statistical mechanics models with non-Hermitian transfer matrices. We discuss a class of Z(N) spin models with explicit PT\mathcal{PT} symmetry and also the ANNNI model, which has a hidden PT\mathcal{PT} symmetry. For both quantum and classical models, the class of models with generalized PT\mathcal{PT} symmetry is precisely the class where the complex weight problem can be reduced to real weights, i.e., a sign problem. The spatial two-point functions of such models can exhibit three different behaviors: exponential decay, oscillatory decay, and periodic behavior. The latter two regions are associated with PT\mathcal{PT} symmetry breaking, where a Hamiltonian or transfer matrix has complex conjugate pairs of eigenvalues. The transition to a spatially modulated phase is associated with PT\mathcal{PT} symmetry breaking of the ground state, and is generically a first-order transition. In the region where PT\mathcal{PT} symmetry is unbroken, the sign problem can always be solved in principle using the equivalence to a Hermitian theory in this region. The ANNNI model provides an example of a model with PT\mathcal{PT} symmetry which can be simulated for all parameter values, including cases where PT\mathcal{PT} symmetry is broken.     

On the symmetries between neutrino and antineutrino-nucleon elastic scattering

Various symmetry relations developed between neutrino-neutron and antineutrino-proton elastic scattering cross sections are surveyed and an identity between scattering amplitudes and a symmetry between cross sections of these processes established by consideringCPT andG conjugation invariance of current matrix elements. A symmetry is obtained giving rise to a theorem on the nature of contribution of form factors to terms in the cross sections.     

Competition mechanism between singlet and triplet superconductivity in the tight-binding model with anisotropic attractive potential

Based upon the tight-binding formalism a model of a high-T_c superconductor with isotropic and anisotropic attractive interactions is considered analytically. Symmetry facets of the group C_4v are included within a method of successive transformations of the reciprocal space. Complete sets of basis functions of C_4v irreducible representations are given. Plausible spin-singlet and spin-triplet superconducting states are classified with regard to the chosen basis functions. It is displayed that pairing interaction coefficients and the dispersion relation, which can be characterized by the parameter η= 2t₁/t₀, have a diverse and mutually competing influence on the value of the transition temperature. It is also shown that in the case of a nearly half-filled conduction band and an anisotropic pairing interaction the spin-singlet d-wave symmetry superconducting state is realized for small values of the parameter η, whereas in the opposite limit, for sufficiently large values, the spin-triplet p-wave symmetry superconducting state has to be formed. This result cannot be obtained within the Van Hove scenario or BCS-type approaches, where the p-wave symmetry superconducting state absolutely dominates. The specific heat jump and the isotope shift as functions of the parameter η are assessed and discussed for the d-wave symmetry singlet and the p-wave symmetry triplet states.     

PT Symmetry in Quantum Field Theory

The Hamiltonian H specifies the energy levels and the time evolution of a quantum theory. It is an axiom of quantum mechanics that H be Hermitian. The Hermiticity of H guarantees that the energy spectrum is real and that the time evolution is unitary (probability preserving). In this talk we investigate an alternative formulation of quantum mechanics in which the mathematical requirement of Hermiticity is replaced by the more physically transparent condition of space-time reflection (PT) symmetry. We show that if the PT symmetry of a Hamiltonian H is not broken, then the spectrum of H is real. Examples of PT-symmetric non-Hermitian Hamiltonians are H=p ²+ix ³ and H=p ²-x ⁴. The crucial question is whether PT-symmetric Hamiltonians specify physically acceptable quantum theories in which the norms of states are positive and the time evolution is unitary. The answer is that a Hamiltonian that has an unbroken PT symmetry also possesses a physical symmetry that we call C. Using C, we show how to construct an inner product whose associated norm is positive definite. The result is a new class of fully consistent complex quantum theories. Observables exhibit CPT symmetry, probabilities are positive, and the dynamics is governed by unitary time evolution.     

Low-lying excited states of quantum antiferromagnets on a triangular lattice

We study low-lying states of theXY and Heisenberg antiferromagnets on a triangular lattice to clarify whether spontaneous symmetry breaking occurs atT=0 in the thermodynamic limit. Approximate forms of low-lying states are proposed, in which degrees of freedom of the sublattice magnetization and of the chirality are separated. These approximate states have a long-range order and twofold structures. It is shown that low-lying states can be accurately described with the present approximation. It has been argued that low-lying states play an important role in symmetry breaking. With the help of this approximation, we discuss the contribution of low-lying states to symmetry breaking of two types, namely creation of the spontaneous sublattice magnetization and the spontaneous chirality. Furthermore, to show evidence for the occurrence of symmetry breaking, we numerically study the low-lying states of finite systems of theXY and Heisenberg antiferromagnets. It is found that the necessary conditions for the symmetry breaking to occur are satisfied in these models.     

<Emphasis Type="Italic">O</Emphasis>(12) limit and complete classification of symmetry schemes in proton-neutron interacting boson model

It is shown that the proton-neutron interacting boson model (pnIBM) admits new symmetry limits withO(12) algebra which breakF spin but preserves theF _z quantum numberM _F. The generators ofO(12) are derived and the quantum numberU ofO(12) for a given boson numberN is determined by identifying the corresponding quasi-spin algebra. TheO(12) algebra generates two symmetry schemes and for both of them, complete classification of the basis states and typical spectra are given. With theO(12) algebra identified, complete classification of pnIBM symmetry limits with goodM _F is established.     

Pseudoscalar Mesons as Goldstone Bosons in Chiral SU(4) ⊗ SU(4) Symmetry

We study the pseudoscalar mesons in the framework of broken chiral SU(4) SU(4) symmetry when the symmetry-breaking Hamiltonian, H_SB, is taken as –(u₀ + cu₈ + du₁₅) and the symmetry of the Hamiltonian is realized in Goldstone-Nambu way. An interesting property of two chimeral SU(4) subgroups and the Goldstone nature of some of the pseudoscalar mesons in certain symmetry limits are exploited to obtain some mass relations and the ratio c/d.     

Unambiguous evidence for extended s-wave pairing symmetry in hole-doped high-temperature superconductors

We have analysed data from angle-resolved photo-emission spectroscopy, Fourier transform scanning tunneling spectroscopy, and low-temperature thermal conductivity for optimally doped Bi₂Sr₂CaCu₂ O _8+y in order to discriminate between d-wave and extended s-wave pairing symmetry. The combined data are inconsistent with d-wave symmetry, but quantitatively consistent with extended s-wave symmetry with eight line nodes. We also explain all phase-sensitive experiments in a consistent manner.     

Si80笼状分子的结构研究

采用基于密度泛函的第一性原理计算方法,构建了Si₈₀笼状分子的模型,并对其结构和电学特性进行了考察. 研究发现,经过结构优化计算,Si₈₀分子从I_h高对称性下降为T_h,但仍然保持较好的笼状结构. 对Si₈₀笼状分子的稳定性、轨道分布和电荷分布等性质进行了分析和讨论. 关键词： 80')" href="#">Si₈₀ 富勒烯 结构     

Symmetry classification of states in high temperature superconductors

The symmetry classification of possible singlet and also triplet states in the case of the 2-dim square lattice, and 3-dim tetragonal and orthorhombic lattices is examined. If particle-hole symmetry is present then an additional symmetry classification is possible. However in the lower symmetry crystal structures that actually occur, no distinction on symmetry grounds can be drawn between usuals-wave, extendeds-wave and some of thed-wave states.     

Grassmann variables on quantum spaces

Attention is focused on antisymmetrized versions of quantum spaces that are of particular importance in physics, i.e. two-dimensional quantum plane, q-deformed Euclidean space in three or four dimensions as well as q-deformed Minkowski space. For each case standard techniques for dealing with q-deformed Grassmann variables are developed. Formulae for multiplying supernumbers are given. The actions of symmetry generators and fermionic derivatives upon antisymmetrized quantum spaces are calculated. The complete Hopf structure for all types of quantum space generators is written down. From the formulae for the coproduct a realization of the L-matrices in terms of symmetry generators can be read off. The L-matrices together with the action of symmetry generators determine how quantum spaces of different type have to be fused together. Arrival of the final proofs: 6 December 2005